Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
def main():
    n = int(input())
    lookup = set()
    k = 1
    while k * (k + 1) // 2 <= n:
        lookup.add(k * (k + 1) // 2)
        k += 1

    ok = False
    for elm in lookup:
        if elm < n:
            if n - elm in lookup:
                ok = True
    if ok:
        print("YES")
    else:
        print("NO")


if __name__ == "__main__":
    main()